Permutations question - help =[ (1 Viewer)

[Finx]

Hi peoples =]

I've been browsing this site for a while now, and I've hit a wall on a permutations+combinations question;

Q: Five-letter words are formed without repetition from the letters in "PHYSICAL". How many have the two vowels occurring next to one another?

My first guess would be to treat the two vowels (A and I) as one unit in the 5-letter word. You would represent them as 2! since they can be placed as A I or I A.

Now that there are 3 spots left and 6 letters remaining for use, you would multiply the 2! by 6P3.

Here I get stuck, I don't know what I have to do next =/

 

[Slidey]

x x x x x

Right?
Now, two vowels next to each other would be of the form:

x x x o

So there are 2*1 ways to arrange the two vowels next to each other, and 4 ways to arrange the vowel pair in the 5-letter word (i.e. o x x x, x o x x, x x o x, x x x o)

And as for the remaining x positions we have 6 * 5 * 4 ways to arrange those letters.

Answer: 6P3 * 4P1 * 2P2

Looks like you were just missing the 4 different positions of the vowel combo in the word, year?

 

[Finx]

Yup.

I got the answer, but in a different format.

Using O X X X

O represents the AI or IA possibility (as 2!)

Then 6*5*4 represents the remaining letters for use (in the X X X position)

So in the case of O X X X, the equation would be 2!*6*5*4

But O can appear in four places in the O X X X word, so I ended up with 2!*6*5*4*4, giving me the correct answer.

Is this way of thinking correct, or did I just get lucky?

 

[tacogym27101990]

same thing

 

[lacklustre]

I'd just like to thank Slidey. Everytime I go through previous threads, he is always there helping us out.

Thanks man for your time.

 

[tacogym27101990]

I'd just like to thank Slidey. Everytime I go through previous threads, he is always there helping us out.

Thanks man for your time.

well said

 

[pLuvia]

It's the same thing

6*5*4 = 6P3
4=4P1

 

[Slidey]

Cheers guys.

And yep, that's spot on Finx, as pLuvia demonstrated.